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VectorCalculus

  

Curl

  

compute the curl of a vector field in R^3

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Curl(F)

Parameters

F

-

(optional) vector field or a Vector valued procedure; specify the components of the vector field

Description

• 

The Curl(F) command computes the curl of the vector field F in R^3.  This is a synonym for Del &x F or CrossProduct(Del, F).

• 

If F is a Vector valued procedure, the default coordinate system is used, and it must be indexed by the coordinate names.  Otherwise, F must be a vector field.

• 

If F is a procedure, the result is a procedure.  Otherwise, the result is a vector field.

• 

The Curl() command returns the differential form of the curl operator in the current coordinate system.  For more information, see SetCoordinates.

Examples

withVectorCalculus:

SetCoordinates'cartesian'x,y,z

cartesianx,y,z

(1)

FVectorFieldy,x,0

F:=ye_xxe_y

(2)

CurlF

2e_z

(3)

Curl

yVF 3x,y,zzVF 2x,y,ze_x+zVF 1x,y,zxVF 3x,y,ze_y+xVF 2x,y,zyVF 1x,y,ze_z

(4)

Del &x F

2e_z

(5)

Nabla &x F

2e_z

(6)

CrossProductDel,F

2e_z

(7)

Curlx,y,z→x2,y2,z2

x,y,z→VectorCalculus:-Vector0,0,0,attributes=vectorfield,coords=cartesianx,y,z

(8)

SetCoordinates'cylindrical'r,θ,z

cylindricalr,θ,z

(9)

Curlr,θ,z→fr,θ,z,gr,θ,z,hr,θ,z

r,θ,z→VectorCalculus:-Vectorθhr,θ,zrzgr,θ,zr,zfr,θ,zrhr,θ,z,gr,θ,z+rrgr,θ,zθfr,θ,zr,attributes=vectorfield,coords=cylindricalr,θ,z

(10)

See Also

VectorCalculus

VectorCalculus[CrossProduct]

VectorCalculus[Del]

VectorCalculus[Divergence]

VectorCalculus[Gradient]

VectorCalculus[Laplacian]

VectorCalculus[SetCoordinates]

VectorCalculus[Vector]

VectorCalculus[VectorField]

Vectors/Curl

 


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